Get yourself a copy of http://www.netfabb.com/basic.php it's free
Click on the red cross. You will see the yellow triangle is a hole and the orange lines are degenerated faces. These can be repaired. The part that is red on top of blue means you have faces on top of each other with no apparent thickness. This cannot be repaired in Netfabb. You need to give this area some thickness to separate the two faces.
It would be wise to overlap the three shells so Shapeways software will join them together as one.

" In short: your mesh is manifold when all vertices are connected with edges and those edges are connected to exactly two faces.
ctrl+alt+shift+m tries to select non-manifold parts of your mesh.
Those parts could be: loose vertices, double geometry, inside faces/edges, holes."
Coplanar faces, separate meshes and ngons can also lead to nonmanifold errors.
A good way to check for overlapping faces in Blender is to go to the property panel/object data and unclick double sided. It is similar to the red area in Jacants picture, except these areas will be darker compared to the rest of the mesh in Blender. This will also show incorrectly oriented normals.
Some tips
When you select non-manifold and the verts get highlighted, you can swap to edge select to clearly define the holes,(should not be creating a plane)
Enabling the measure panel addon will calculate volume, surface area, will tell you if the mesh is nonmanifold and if ngons are present.The settings are in the Npanel. As is display normals.
Experiment with the select similar options for faces,verts and edges. This helps in repair also.

Was this a file from something scanned?

Keith

Have any questions regarding Blender, and need fast answers, you are always welcome at the IRC Server Freenode, channel #blender. As a bonus, several there have experience in modelling for 3D prints.